Approximability of the independent feedback vertex set problem for bipartite graphs

Yuma Tamura; Takehiro Ito; Xiao Zhou

doi:10.1007/978-3-030-39881-1_24

Approximability of the independent feedback vertex set problem for bipartite graphs

Yuma Tamura, Takehiro Ito, Xiao Zhou

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n^1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.

Original language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
Editors	M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
Publisher	Springer
Pages	286-295
Number of pages	10
ISBN (Print)	9783030398804
DOIs	https://doi.org/10.1007/978-3-030-39881-1_24
Publication status	Published - 2020 Jan 1
Event	14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore Duration: 2020 Mar 31 → 2020 Apr 2

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12049 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
Country	Singapore
City	Singapore
Period	20/3/31 → 20/4/2

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-39881-1_24

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Cite this

Tamura, Y., Ito, T., & Zhou, X. (2020). Approximability of the independent feedback vertex set problem for bipartite graphs. In M. S. Rahman, K. Sadakane, & W-K. Sung (Eds.), WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings (pp. 286-295). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12049 LNCS). Springer. https://doi.org/10.1007/978-3-030-39881-1_24

Approximability of the independent feedback vertex set problem for bipartite graphs. / Tamura, Yuma; Ito, Takehiro ; Zhou, Xiao.

WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. ed. / M. Sohel Rahman; Kunihiko Sadakane; Wing-Kin Sung. Springer, 2020. p. 286-295 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12049 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Tamura, Y, Ito, T & Zhou, X 2020, Approximability of the independent feedback vertex set problem for bipartite graphs. in MS Rahman, K Sadakane & W-K Sung (eds), WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12049 LNCS, Springer, pp. 286-295, 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020, Singapore, Singapore, 20/3/31. https://doi.org/10.1007/978-3-030-39881-1_24

Tamura Y, Ito T , Zhou X. Approximability of the independent feedback vertex set problem for bipartite graphs. In Rahman MS, Sadakane K, Sung W-K, editors, WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. Springer. 2020. p. 286-295. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-39881-1_24

Tamura, Yuma ; Ito, Takehiro ; Zhou, Xiao. / Approximability of the independent feedback vertex set problem for bipartite graphs. WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. editor / M. Sohel Rahman ; Kunihiko Sadakane ; Wing-Kin Sung. Springer, 2020. pp. 286-295 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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